INTRODUCTORY STATISTICS


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1 INTRODUCTORY STATISTICS FIFTH EDITION Thomas H. Wonnacott University of Western Ontario Ronald J. Wonnacott University of Western Ontario WILEY JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore
2 CONTENTS PART I BASIC PROBABILITY AND STATISTICS 1 The Nature of Statistics 11 Random Sampling: A Political Poll 12 Randomized Experiments: Testing a Hospital Routine Observational Studies vs. Randomized Experiments Brief Outline of the Book 20 Chapter 1 Summary 20 2 Descriptive Statistics 21 Frequency Tables and Graphs Center of a Distribution Spread of a Distribution Statistics by Computer Linear Transformations Calculations Using Relative Frequencies The Use and Misuse of Graphs 53 Chapter 2 Summary 64 3 Probability 31 Introduction Probability Models Compound Events Conditional Probability Independence Bayes Theorem: Tree Reversal Other Views of Probability 99 Chapter 3 Summary Probability Distributions 41 Discrete Random Variables Mean and Variance The Binomial Distribution Continuous Distributions The Normal Distribution A Function of a Random Variable 134 *47 Expected Value in Bidding 141 Chapter 4 Summary Two Random Variables Distributions A Function of Two Random Variables Covariance Linear Combination of Two Random Variables 170 Chapter 5 Summary 176 Review Problems (Chapters 15) 182 PART II INFERENCE FOR MEANS AND PROPORTIONS Sampling Random Sampling Moments of the Sample Mean The Shape of the Sampling Distribution Proportions (Percentages) 207 *65 SmallPopulation Sampling 215 *66 Monte Carlo 218 Chapter 6 Summary Point Estimation Populations and Samples Efficiency of Unbiased Estimators Efficiency of Biased and Unbiased Estimators 239 *74 Consistent Estimators 244 Chapter 7 Summary 248 XIII
3 XIV CONTENTS 8 Confidence Intervals A Single Mean SmallSample t Difference in Two Means, Independent Samples Difference in Two Means, Matched Samples Proportions 273 *86 The Bootstrap 277 Chapter 8 Summary Hypothesis Testing Hypothesis Testing Using Confidence Intervals pvalue (OneSided) Classical Hypothesis Tests 300 *94 Classical Tests Reconsidered 306 *95 Operating Characteristics Curve (OCC) 310 *96 TwoSided Tests 314 Chapter 9 Summary Analysis of Variance (ANOVA) OneWay ANOVA TwoWay ANOVA Confidence Intervals 343 Chapter 10 Summary 346 Review Problems (Chapters 610) Confidence Intervals and Tests for p Predicting Vat a Given Level of X Extending the Model 389 Chapter 12 Summary Multiple Regression Why Multiple Regression? The Regression Model and Its OLS Fit Confidence Intervals and Statistical Tests Regression Coefficients as Multiplication Factors 410 *135 Simple and Multiple Regression Compared 417 *136 Path Analysis 424 Chapter 13 Summary Regression Extensions Dummy (01) Variables Analysis of Variance (ANOVA) by Regression Simplest Nonlinear Regression 449 *144 Nonlinearity Removed by Logs 452 *145 Diagnosis by Residual Plots 461 Chapter 14 Summary Correlation 474 PART III REGRESSION: RELATING TWO OR MORE VARIABLES Fitting a Line Introduction Ordinary Least Squares (OLS) Advantages of OLS and WLS 366 Chapter 11 Summary Simple Correlation Correlation and Regression 153 The Two Regression Lines Correlation in Multiple Regression Multicollinearity 501 Chapter 15 Summary 506 Review Problems (Chapters 1115) Simple Regression The Regression Model Sampling Variability 375 PART IV TOPICS IN CLASSICAL AND BAYESIAN INFERENCE 515
4 CONTENTS XV 16 Nonparametric and Robust Statistics (Requires Chapter 9) Introduction: Mean or Median? Sign Test for the Median Confidence Interval for the Median Wilcoxon Rank Test Rank Tests in General Runs Test for Independence Robust Statistics: Trimming and Weighting 536 Chapter 16 Summary ChiSquare Tests (Requires Chapter 9) x 2 Tests for Multinomials: Goodness of Fit x 2 Tests for Independence: Contingency Tables 555 Chapter 17 Summary 561 *18 Maximum Likelihood Estimation (Requires Chapter 7) Introduction MLE for Some Familiar Cases MLE for the Uniform Distribution MLE in General 576 Chapter 18 Summary 579 *19 Bayesian Inference (Requires Chapter 8) Posterior Distributions The Population Proportion The Mean ^ in a Normal Model The Slope /3 in Normal Regression Bayesian Shrinkage Estimates Classical and Bayesian Estimates Compared 615 Chapter 19 Summary 615 *20 Bayesian Decision Theory (Requires Chapter 19) 201 Maximizing Gain (or Minimizing Loss) Point Estimation as a Decision Classical and Bayesian Statistics Compared 633 Chapter 20 Summary 635 * Appendixes 22 Careful Approximation of the Median 638 N 25 Effects of a Liriear Transformation* Proofs Probability as Axiomatic Mathematics Easier Formula for o 2 : Proof Binomial Formula: Proof Calculus for Continuous Distributions Independent Implies Uncorrelated: Proof Linear Combinations: Proofs Central Limit Theorem Continuity Correction: Graphical Explanation 643 ( 72 Standard Error of X Consistency: Careful Definition Standard Error of (X,  X 2 ): Proof Confidence Interval for w. Derivation of Graph A More Exact pvalue for Proportions Breakdown of Total SS: Proof TwoWay ANOVA, Breakdown of Total SS: Proof ANOVA Is Much More Than Just Testing H o Lines and Planes LeastSquares Formulas: Proofs The Moments of fa: Proofs and Discussion A Onesided or Twosided Test?
5 XVI CONTENTS 124 Confidence Intervals above X o : Proofs Solution of a Set of Simultaneous Equations Direct Plus Indirect Relation: Proof Log Regression Handles a Multiplicative Error Term Correlation in Chapter 15 Agrees with Chapter ANOVA and r 2 : Proofs MLE for Some Familiar Cases: Proofs Bayesian Confidence Interval fortr Proof Posterior Distribution of fi in a Normal Model: Proof Posterior Distribution of j8 in Normal Regression: Proof Bayesian Shrinkage Confidence Intervals 662 Tables 663 References 679 Answers to OddNumbered Problems 685 Glossary of Common Symbols 699 Index of Examples and Problems 703 index 705
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